Every month $40 is withdrawn from Toms savings account to pay for his gym membership. He has enough savings to withdrawn no more than $360. For how many months can Tom pay for his gym membership?

Question is Incomplete; Complete question is given below;

Johnny must learn more than 10 new plays before the big game. He has already learned 4. Write and solve the inequality that represents how many more plays he needs to learn to reach his goal?

Answer:

The Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].

Johnny should learn more than 6 games to reach his goals.

Step-by-step explanation:

Given:

Number of plays to be learn [tex]>[/tex] 10

Number of plays already learned = 4

we need to write an inequality that represents how many more plays he needs to learn to reach his goal.

Solution:

Let the number of plays needed to learn more be 'x'.

So we can say that;

Number of plays already learned plus number of plays needed to learn more should be greater than total Number of plays to be learn.

framing in equation form we get;

[tex]x+4>10[/tex]

Hence the Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].

On solving the equality we get;

Subtracting both side by 4 we get;

[tex]x+4-4>10-4\\\\x>6[/tex]

Hence Johnny should learn more than 6 games to reach his goals.

Final answer:

By setting up an equation using the average weight formula and solving for x, we find that x equals 5. Subsequently, the heavier carton weighs 13 pounds, and the lighter carton weighs 7 pounds, making the heavier carton weigh 6 pounds more than the lighter carton.

Explanation:

The question involves finding out how many more pounds the heavier carton weighs compared to the lighter carton when given their weights in terms of x and the average weight.

Firstly, we are given that the weights of the two cartons are 3x - 2 and 2x - 3 pounds, and their average weight is 10 pounds.

To find the value of x, we need to set up an equation using the average weight formula, which is:

(Weight of Carton 1 + Weight of Carton 2) / 2 = Average Weight

Substituting the given weights and average weight into the formula, we get:

((3x - 2) + (2x - 3)) / 2 = 10

Solving the equation by combining like terms and multiplying both sides by 2 to eliminate the fraction gives:

5x - 5 = 20

Adding 5 to both sides and then dividing by 5:

x = 5

Now, let's find the actual weight of each carton:

Weight of the first carton = 3x - 2 = 3(5) - 2 = 13 pounds

Weight of the second carton = 2x - 3 = 2(5) - 3 = 7 pounds

Lastly, we determine how many more pounds the heavier carton weighs compared to the lighter one:

13 pounds - 7 pounds = 6 pounds

Therefore, the heavier carton weighs 6 pounds more than the lighter carton.

Answer:

x             frequency

4.8        1

4.83       1

4.85     2

4.89     1

4.91     1

4.94    2

4.96   1

4.99   1

5.04    3

5.05    1

5.12    3

5.14   1

5.15   1

5.17   1

5.19   2

5.24    1

5.26     1

5.27     1

5.28     1

find the dot plot as attached below

Step-by-step explanation:

Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26

Rearranging the data into frequency table

x             frequency

4.8        1

4.83       1

4.85     2

4.89     1

4.91     1

4.94    2

4.96   1

4.99   1

5.04    3

5.05    1

5.12    3

5.14   1

5.15   1

5.17   1

5.19   2

5.24    1

5.26     1

5.27     1

5.28     1

Answer: Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.

Step-by-step explanation:

Let x be the grades scored by Mary in the fourth algebra test.

Mary has grades of 95, 82, 88 on her first three algebra tests.

Then, the combined scores in four test will become = 95+82+88+x =  265+x

Average score = (Sum of all scores) ÷ (Number of tests)

[tex]=\dfrac{265+x}{4}[/tex]

As per given ,

To earn an A in an algebra course, a student must have a test average of at least 90.

i.e. Average score ≥ 90

[tex]\Rightarrow\ \dfrac{265+x}{4}\geq90\\\\\Rightarrow\ 265+x\geq 90\times4=360\\\\\Rightarrow\ x\geq360-265 =95\\\\\Rightarrow\ x\geq90[/tex]

Hence, Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.

Answer:

Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.

Step-by-step explanation:

Let the cost of queen-size burger be 'q'.

Let the cost of steak-in-a-bun be 's'.

Given:

a steak-in-a-bun cost $0.90 more than a queen-size burger.

So we can say that;

[tex]s=0.9+q \ \ \ \ equation\ 1[/tex]

Given:

the coach took ten students to burger box.

Hence Number of person at burger box = 11

The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers.

So we can say that;

Number of queen sized burger = 11 - 4 =7

Number of steak on a bun burger = 4

Also Given:

Total bill = $15.11

Now we can say that;

Total bill is equal to sum of Number of queen sized burger multiplied by Cost of queen sized burger and Number of steak on a bun burger multiplied by cost of steak on a bun burger.

framing in equation form we get;

[tex]4s+7q =15.15\ \ \ \ equation\ 2[/tex]

Substituting equation 1 in equation 2 we get;

[tex]4(0.9+q)+7q=15.15[/tex]

Applying distributive property we get;

[tex]3.6+4q+7q=15.15\\\\3.6+11q=15.15[/tex]

Subtracting both side by 3.6 we get;

[tex]3.6+11q-3.6 =15.15-3.6\\\\11q=11.55[/tex]

Dividing both side by 11 we get;

[tex]\frac{11q}{11}=\frac{11.55}{11}\\\\q=\$1.05[/tex]

Substituting the value of q in equation 1 we get;

[tex]s=0.9+q=0.9+1.05=\$1.95[/tex]

Hence Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.

Final answer:

The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.

Explanation:

The student's question involves finding the cost of one steak-on-a-bun and one queen-size burger given that the total bill for a group order at a restaurant was $15.15 and that a steak-on-a-bun costs $0.90 more than a queen-size burger.

Let's define Q as the price of a queen-size burger.

Therefore, the price of a steak-on-a-bun would be Q + $0.90. According to the problem, four people (the coach and three students) ordered steak-on-a-bun, and six students ordered queen-size burgers.

The equation representing the total cost is:

4(Q + $0.90) + 6Q = $15.15

Solving for Q, we first expand the equation:

4Q + $3.60 + 6Q = $15.15

Combining like terms, we get 10Q + $3.60 = $15.15.

Subtracting $3.60 from both sides, we get 10Q = $11.55.

Dividing both sides by 10, we find that Q = $1.155, which is the cost of a queen-size burger.

Finally, the cost of a steak-on-a-bun is Q + $0.90 = $1.155 + $0.90 = $2.055.

The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.

Answer:

y = (7/8)x

Step-by-step explanation:

Exponential decay is represented when the number used is less than 1. 7/8 is the only choice that is less than 1.

y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.

An exponential decay is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier which is less than 1.

From the question y = (7/8)ˣ is an exponential decay because b = 7/8 < 1.

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The histogram depicts the year-by-year damage in millions of dollars caused by tornadoes from 1950 to 1999. It uses class intervals to display the frequency of damage costs, where each bar represents a specific cost range.

In the given question, we discuss a histogram that represents the commutative property damage caused by tornadoes from 1950 to 1999 across the 50 US states and Puerto Rico. The histogram's class intervals are set from 0 to < 10, 10 to < 20, and so forth, and the data are in millions of dollars. A histogram is a type of graphical representation used in statistics to display the distribution of data. Each bar in a histogram represents the tabulated frequency at each interval. In this case, the frequency is the year count in which the commutative property damage caused by tornadoes falls within a specific monetary range.

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Answer:

Step-by-step explanation:

The cost of the three books that James bought from the bookstore.

He has a coupon for 25% off the original price. This means that the amount by which the original price was reduced would be

25/100 × 39.99 = 0.25 × 39.99 = $9.8325

The cost of the books would be

39.99 - 9.8325 = $30.1575

He is charged 8.5% sales tax. This means that the amount paid for tax would be

8.5/100 × 30.1575 = 0.085 × 30.1575 = $2.56

the total cost of his purchase would be

2.56 + 30.1575 = $32.7175

Answer:

$32.7175

Step-by-step explanation:

Answer:

f(-1) = 10

Step-by-step explanation:

f(x)=x² - 3x + 6

when x = -1, substitute x=-1 into the equation above

f(-1) = (-1)² - 3(-1) + 6

= 1 + 3+6

= 10

Answer:

He has 2 quarters in his pocket.

Answer:it will take 1850 miles

Step-by-step explanation:

Let x represent the number of miles in a day at which the rental costs for a company A and Company B same.

Let y represent the total cost of renting the truck for x miles with company A.

Let z represent the total cost of renting the truck for x miles with company A.

Company A charges $420 a day Plus $.30 per mile. This means that

y = 420 + 0.3x

Company B charges $50 a day plus $.50 per mile to rent the same truck. This means that

z = 50 + 0.5x

To determine the number of miles in a day at which the rental costs for a company A and Company B same, we will equate y to z. It becomes

420 + 0.3x = 50 + 0.5x

0.5x - 0.3x = 420 - 50

0.2x = 370

x = 370/0.2 = 1850 miles

To find the value of x for the corresponding sides of two similar triangles, we set up a proportion using the given sides.

Upon simplifying the ratio, x is calculated to be 24, which is the side length in the second triangle.

To find the value of x in two similar triangles with side lengths 12, 15, 18 and 16, 20, x, we use the concept that corresponding sides in similar triangles have proportional lengths.

We start by setting up a proportion using the corresponding sides:

[tex]\(\frac{12}{16} = \frac{15}{20} = \frac{18}{x}\)[/tex]

We can simplify the first two ratios to find a single scale factor:

[tex]\(\frac{12}{16} = \frac{15}{20} \rightarrow \frac{3}{4} = \frac{3}{4}\)[/tex]

This confirms the triangles are indeed similar since the ratios are equal. We then use the third ratio to solve for x:

[tex]\(\frac{18}{x} = \frac{3}{4} \rightarrow x = \frac{4}{3} \cdot 18 = 24\)[/tex]

Therefore, the value of x is 24, which is the length of the corresponding side in the second triangle.

Answer:

5 times the square root of 3

Step-by-step explanation:

To get the longest side of a 30-60-90 triangle, you take the shortest side and multiply it by the square root of 3.

5*(square root of 3)

Answer: 17.3

Step-by-step explanation:

Since it is a right angled triangle , we will use the application of SOHCAHTOA in solving it  ,which means

sine Ф = opposite / hypotenuse

cosine Ф = adjacent / hypotenuse

Tangent Ф = opposite / adjacent

Ф stands for the given angle.

From the diagram , the given angle is 25 ,this means that

opposite = x

hypotenuse = 41

This means that we will use sine Ф = opposite / hypotenuse to find the value of x.

Therefore:

sin 25 = x/41

x = 41 sin 25

x = 41 x 0.4226

x = 17.3273

x ≈ 17.3

Answer:

Explanation:

The image attached shows the dimensions of the coffe cans considered for this question.

The figure is a cylinder with dimensions:

Thus, to find the lateral surface of a coffe can, you use the formula for the lateral area of a cylinder:

Where, LA is the lateral area, r is the radius, and h is the height.

Substituting the dimensions given in the figure, you get:

To multiply, first convert the mixed numbers into improper fractions:

[tex]3\frac{1}{16}=3+\frac{1}{16}=\frac{3(16)+1}{16}=\frac{48+1}{16}=\frac{49}{16}\\ \\ 6\frac{5}{8}=6+\frac{5}{8}=\frac{6(8)+5}{8}=\frac{48+5}{8}=\frac{53}{8}[/tex]

Now, you can multiply:

Answer:

Cost per Electricity Unit= $0.61

Cost per Gas Unit= $0.22

Step-by-step explanation:

Suppose,

Cost per Electricity Unit: e

Cost per Gas Unit: g

for the first month condition, equation would be

[tex]600*e+100*g=388...........................................(i)[/tex]

and for the next month condition, equation would be like

[tex]400*e+150*g=277...........................................(ii)[/tex]

By solving both linear equations simultaneously, we get

e=0.61    and     g=0.22

Answer:

[tex]g(x)=|x+4|-2[/tex]

Step-by-step explanation:

All the absolute value functions given in the option are of the form:

[tex]g(x)=|x-h|+k[/tex], where (h,k) is the vertex

From your description the absolute value graph has vertex at (-4,-2)

Hence h=-4 and k=-2.

We substitute to get:

[tex]g(x)=|x--4|+-2[/tex]

We simplify to get:

[tex]g(x)=|x+4|-2[/tex]

Answer:

In step 2, the LCD was not used correctly to make equivalent fractions.

Step-by-step explanation:

Answer:

In step 2, the LCD was not used correctly to make equivalent fractions.

Step-by-step explanation:

The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.

The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:

p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x

So the price can be represented by the equation p(x) = 505 - 2x.

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Answer:

a) 1805.55$

b) 2.14$

c)0.005$

d)0.064$

e)1805.55$

Step-by-step explanation:

Density of mercury is 844.9 lb/ft3.

a) 76 pound flask of mercury is 76/844.9=0.09 ft^3. 0.09 ft^3 mercury cost 162.5$, then 1 ft^3 mercury is

[tex]p=(162.5/0.09)=1805.55[/tex]

1805.55$

b) One pound of mercury is 2.14$

[tex]p=162.5/76=2.14[/tex]

c)76 pound equals 34473 grams. It makes:

[tex]p=162.5/34473=0.005[/tex]

0.005$ is the price of one gram mercury.

d)Total amount of mercury is 34473 grams. Then total volume of mercury is:

[tex]V=34473/13.534=2547.14[/tex]

2547.14 cm3. And the unit price is:

[tex]p=162.5/2547.14=0.064[/tex]

e) 1805.55$. It is found already.

Attached is a graph of the function [tex]f(x)=\sqrt{9}[/tex]

Answer:445 student tickets were sold.

75 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of student tickets that were sold in the talent show.

Let y represent the number of adult tickets that were sold in the talent show.

The talent show committee sold a total of 530 tickets in advance. This means that

x + y = 530

Student tickets cost $3 each and the adult tickets cost $5 each. The total receipts were $1740. This means that

3x + 5y = 1740 - - - - - - - - - - - - 1

Substituting x = 530 - y into equation 1, it becomes

3(530 - y) + 5y = 1740

1590 - 3y + 5y = 1740

- 3y + 5y = 1740 - 1590

2y = 150

y = 150/2 = 75

x = 530 - y = 530 - 75

x = 455

.

Answer:

Continuous observation

Step-by-step explanation:

Generally, the weight of any person is displaced in whole numbers without the inclusion of decimal numbers. The decimal numbers are mostly rounded up to the whole number. Based on the argument made in the given problem, the type of weight variable for this type of analysis is known as continuous observation.

Answer: the top of the ladder is 20ft below the ground.

Step-by-step explanation:

The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.

The length of the ladder represents the hypotenuse of the right angle triangle.

The ground distance between the base of the house and the base of the ladder represents the adjacent side of the right angle triangle.

Therefore, to determine the height at which the ladder rest on the building, x, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

25² = x² + 15²

625 = x² + 225

x² = 625 - 225 = 400

x = √400 = 20 ft

Answer:

Step-by-step explanation:

2.75×100=275.00

3=3.00×100=100.00

in either case decimal point moves to the right.

but in whole numbers 3=3

Answer:

a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]

b) Matrix AB = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]

c) $12,695

Step-by-step explanation:

Matrix A = [tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex]

a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]

Gross Receipt = AB

[tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex] . [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex] = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]

c) Total revenue is the sum of receipts from 4 cinemas given in part b

Hence,

Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695

Answer: c. 72% is a statistic and 56% is a parameter.

Step-by-step explanation:

Given : A study of voting chose 663 registered voters at random shortly after an election.

Population of interest : "registered voters"

Sample : " 663 registered voters "

72%  of 663 registered voters said they had voted in the election.

⇒ Statistic = sample proportion registered voters voted in the election.= 72%

Election records show that only 56% of registered voters voted in the election.

⇒ Parameter = Population proportion of registered voters voted in the election =  56%

Hence, the correct answer is "c. 72% is a statistic and 56% is a parameter."

Answer:the total cost of the collar is $5.11

Step-by-step explanation:

To make a collar for her dog, she needs to buy some chain,a clasp, and a name tag.

The length of the chain that she wants to buy is 40 centimeters.

1000 centimeters = 1 meter

40 centimeters = 40/1000 = 0.04 meters.

One meter of chain costs $9.75. Therefore, 0.04 meters of chain would cost

0.04 × 9.75 = $0.39

The clasp is $1.29 and the name tag is $3.43. Therefore, the total cost of the collar would be

0.39 + 1.29 + 3.43 = $5.11

Answer:

Below.

Step-by-step explanation:

a  = tangential velocity

b  = tangential acceleration

c  = Angular acceleration

d  = angular displacement

e  =  Angular velocity

f   =   radius.

Question is Incomplete;Complete question is given below;

Caleb made $105 mowing lawns and walking dogs, charging the rates shown. If he mowed half as many lawns as dogs walked, how many lawns did he mow and how many dogs did he walk? $7.50 for walking dogs and $20 for mowing lawns

Answer:

Caleb mowed 3 lawns and walked 10 dogs.

Step-by-step explanation:

Let the number of dogs he walked be 'd'.

Let number of lawn he mowed be 'l'.

Given:

If he mowed half as many lawns as dogs walked

So we can say that;

[tex]l=\frac{1}{2}d=0.5d \ \ \ \ equation\ 1[/tex]

Now given:

Cost for mowing each lawn = $20

Cost for walking each dog = $7.50

Total amount made = $105

Now we can say that;

Total amount made is equal to Cost for mowing each lawn multiplied by number of lawn he mowed and Cost walking each dog multiplied by number of lawn he mowed.

framing in equation form we get;

[tex]20l+7.5d=105 \ \ \ \ \ equation \ 2[/tex]

Substituting equation 1 in equation 2 we get;

[tex]20(0.5d)+7.5d=105[/tex]

Applying distributive property we get;

[tex]10d+7.5d=105\\\\17.5d=105[/tex]

Dividing both side by 17.5 we get;

[tex]\frac{17.5d}{17.5}=\frac{105}{17.5}\\\\d= 6[/tex]

Substituting the value of 'd' in equation 1 we get;

[tex]l=0.5d=0.5\times6=3[/tex]

Hence Caleb mowed 3 lawns and walked 10 dogs.